5(8-12x)=6x(4-10x)

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Solution for 5(8-12x)=6x(4-10x) equation: 


Simplifying
5(8 + -12x) = 6x(4 + -10x)
(8 * 5 + -12x * 5) = 6x(4 + -10x)
(40 + -60x) = 6x(4 + -10x)
40 + -60x = (4 * 6x + -10x * 6x)
40 + -60x = (24x + -60x2)

Solving
40 + -60x = 24x + -60x2

Solving for variable 'x'.

Combine like terms: -60x + -24x = -84x
40 + -84x + 60x2 = 24x + -60x2 + -24x + 60x2

Reorder the terms:
40 + -84x + 60x2 = 24x + -24x + -60x2 + 60x2

Combine like terms: 24x + -24x = 0
40 + -84x + 60x2 = 0 + -60x2 + 60x2
40 + -84x + 60x2 = -60x2 + 60x2

Combine like terms: -60x2 + 60x2 = 0
40 + -84x + 60x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(10 + -21x + 15x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(10 + -21x + 15x2)' equal to zero and attempt to solve:

Simplifying
10 + -21x + 15x2 = 0

Solving
10 + -21x + 15x2 = 0

Begin completing the square.  Divide all terms by
15 the coefficient of the squared term: 

Divide each side by '15'.
0.6666666667 + -1.4x + x2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + -1.4x + -0.6666666667 + x2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + -1.4x + x2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + -1.4x + x2 = 0 + -0.6666666667
-1.4x + x2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
-1.4x + x2 = -0.6666666667

The x term is -1.4x.  Take half its coefficient (-0.7).
Square it (0.49) and add it to both sides.

Add '0.49' to each side of the equation.
-1.4x + 0.49 + x2 = -0.6666666667 + 0.49

Reorder the terms:
0.49 + -1.4x + x2 = -0.6666666667 + 0.49

Combine like terms: -0.6666666667 + 0.49 = -0.1766666667
0.49 + -1.4x + x2 = -0.1766666667

Factor a perfect square on the left side:
(x + -0.7)(x + -0.7) = -0.1766666667

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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